Umbrella Sampling Technique Research Articles

Characterization of the Interactions of Arg-Gly-Asp- and Ala-Gly-Asp-Val-Containing Peptides with the Platelet Integrin αIIbβ3

Binding of soluble fibrinogen to the activated open conformation of the integrin αIIbβ3 is required for platelet aggregation and is mediated exclusively by the C-terminal AGDV-containing dodecapeptide (γC-12) sequence of the fibrinogen γ chain. Paradoxically, however, peptides containing the Arg-Gly-Asp (RGD) sequences located in two places in the fibrinogen Aα chain inhibit soluble fibrinogen binding to αIIbβ3. Moreover, the Aα chain RGD motifs make substantial contributions to αIIbβ3 binding when fibrinogen is immobilized and when it is converted to fibrin. The interaction of αIIbβ3 with a variety of RGD- and γC-12 peptides has been studied extensively, but the characteristics of their binding to the active open and inactive closed conformations of αIIbβ3 are largely unknown. Here, we have used both experimental and computational approaches to compare the two-dimensional kinetics, thermodynamics and structural details of cyclic RGDFK (cRGDFK) and γC-12 binding to αIIbβ3. First, we employed optical trap-based single-molecule nanomechanical measurements to determine the probability of peptide binding to αIIbβ3 as a function of the time the peptides interact with αIIbβ3. In the optical trap-based experimental system, a microscopic bead coated with either cRGDFK or γC-12 is trapped in a fluid chamber by a focused laser beam and moved in an oscillatory manner to touch a stationary pedestal coated with αIIbβ3. When the peptide on the bead interacts with αIIbβ3 on the pedestal, tension is generated when the bead is displaced from the laser focus until the αIIbβ3-peptide bond ruptures. The percentage of binding/unbinding events at a particular time of contact duration enabled us to plot the force-free binding probability as a function of contact duration. From these curves, we extracted first-order binding rates: 0.61×10-14 cm2/s for γC-12 and 0.71×10-14 cm2/s for cRGDFK and unbinding rates: 2.05/s and 1.53/s for the γC-12 and cRGDFK, respectively. Corresponding binding affinity constants were 0.3×10-14 cm2 and 0.46×10-14 cm2 for the γC-12 and cRGDFK, respectively, indicating that cRGDFK binds to αIIbβ3 somewhat tighter than γC-12. These measurements were then followed by computational modeling using NMR-determined 3D solution structures of cRGDFK and γC-12, as well as the crystallographically resolved αIIbβ3 conformers of the αIIbβ3 headpiece (PDB entries: 3ZDX and 3ZE2). Docking analysis confirmed that both cRGDFK and γC-12 bound to the αIIbβ3 conformers at a site located in the interface between the α subunit β-propeller domain and the β subunit βI domain. Estimated docking energies revealed that the closed αIIbβ3 conformation is almost as reactive towards the peptides as the open conformation. Next, we probed the strength of the αIIbβ3-peptide interactions and determined their comparative binding energies and the dynamics of interatomic contacts by performing dynamic force-ramp unbinding in silico using all-atom Molecular Dynamics simulations in implicit solvent on Graphics Processing Units. Force was increased linearly at a pulling rate of 2×104 μm/s and applied to specified Cα-atom of the peptides. Analysis of the molecular force profiles and the number of ligand-receptor binding contacts revealed that both peptides interact strongly with αIIbβ3, forming stable bimolecular complexes that dissociate in the 60-120 pN range through several competing unbinding pathways that display multi-step kinetics and distinct bond lifetimes. We profiled the Gibbs free energy (ΔG) of the αIIbβ3-peptide complexes as a function of the separation distance between the open form of αIIbβ3 headpiece and the peptide using the Umbrella Sampling technique. The results showed that the energies of ligand binding to the αIIbβ3 headpiece are ΔG~16 kcal/mol for cRGDFK and ΔG~13 kcal/mol for γC-12, meaning that the overall thermodynamic stability of the αIIbβ3-peptide complex is higher for cRGDFK than for γC-12. Thus, these results provide a kinetic and thermodynamic explanation for previous observations that the affinity of RGD for αIIbβ3 is greater than AGDV and support our hypothesis that the RGD motifs preferentially support the interaction of αIIbβ3 with immobilized fibrinogen and fibrin. DisclosuresWeisel:Bayer: Research Funding.

Partitioning into Colloidal Structures of Fasted State Intestinal Fluid Studied by Molecular Dynamics Simulations.

We performed molecular dynamics (MD) simulations to obtain insights into the structure and molecular interactions of colloidal structures present in fasted state intestinal fluid. Drug partitioning and interaction were studied with a mixed system of the bile salt taurocholate (TCH) and 1,2-dilinoleoyl-sn-glycero-3-phosphocholine (DLiPC). Spontaneous aggregation of TCH and DLiPC from unconstrained MD simulations at the united-atom level using the Berger/Gromos54A7 force fields demonstrated that intermolecular hydrogen bonding between TCH molecules was an important factor in determining the overall TCH and DLiPC configuration. In bilayered systems, these intermolecular hydrogen bonds resulted in embedded transmembrane TCH clusters. Free energy simulations using the umbrella sampling technique revealed that the stability of these transmembrane TCH clusters was superior when they consisted of 3 or 4 TCH per bilayer leaflet. All-atom simulations using the Slipids/GAFF force fields showed that the TCH embedded in the bilayer decreased the energy barrier to penetrate the bilayer (ΔGpen) for water, ethanol, and carbamazepine, but not for the more lipophilic felodipine and danazol. This suggests that diffusion of hydrophilic to moderately lipophilic molecules through the bilayer is facilitated by the embedded TCH molecules. However, the effect of embedded TCH on the overall lipid/water partitioning was significant for danazol, indicating that the incorporation of TCH plays a crucial role for the partitioning of lipophilic solutes into e.g. lipidic vesicles existing in fasted state intestinal fluids. To conclude, the MD simulations revealed important intermolecular interactions in lipidic bilayers, both between the bile components themselves and with the drug molecules.

Passive Transmembrane Permeation Mechanisms of Monovalent Ions Explored by Molecular Dynamics Simulations.

Passive or unassisted ion permeation through lipid bilayers involves a type of rare events by which cells regulate their salt concentrations and pH. It is important to understand its mechanism in order to develop technologies of, for example, delivering or maintaining small drug-like molecules inside cells. In earlier simulations of passive ion permeations, the commonly used sampling methods usually define the positions of ions relative to the membrane as a measure of permeation, i.e., the collective variable, ignoring the active participations of other particles. Newly defined collective variables involving the movements of ions, lipids, and water molecules allow us to identify the transition paths on the free energy landscape using the 2D umbrella sampling techniques. In this work, this technique was used to study the permeation processes of some well-known ions, sodium, potassium, and chloride. It is found permeations of sodium and potassium are assisted by important lipid bilayer deformations and massive water solvation, while chloride may not. Chloride may have two different possible pathways, in which the energetic favorable one is similar to the solubility-diffusion model. The free energy barriers for the permeation of these ions are in semiquantitative agreement with experiments. Further analyses on the distributions of oxygens and interaction energies suggest the electrostatic interactions between ions and polar headgroups of lipids may greatly influence membrane deformation as well as the water wire and furthermore the free energy barriers of waterwire mediated pathways. For chloride, the nonwaterwire pathway may be energetically favorable.

Destabilization of Hydrophobic Core of Chicken Villin Headpiece in Guanidinium Chloride Induced Denaturation: Hint of π-Cation Interaction.

Despite their routine use as protein denaturants, the comprehensive understanding of the molecular mechanisms by which urea and guanidinium chloride (GdmCl) disrupts proteins' structure is still lacking. Here, we use steered molecular dynamics simulations along with the umbrella sampling technique to elucidate the mechanism of unfolding of chicken villin headpiece (HP-36) in these two denaturants. We find that while urea denatures protein predominantly by forming hydrogen bonds with the protein backbone, GdmCl commences unfolding by weakening of the hydrophobic interactions present in the core. The potential of mean force calculation indicates the reduction of hydrophobic interactions between two benzene moieties in 6 M GdmCl as compared to 6 M urea. We observe a near parallel orientation between the guanidinium cation and aromatic side chains of the HP-36 suggesting π-cation type stacking interactions which play a crucial role in weakening of the hydrophobic interaction. We use QM/MM optimization calculations to estimate the energetics of this π-cation interaction. Additionally, the consistency of the unfolding paths between high temperature (400 K) unfolding simulations and steered molecular dynamics simulations strengthens the proposed molecular mechanism of unfolding further.

Composition dependence of the glass forming ability in binary mixtures: The role of demixing entropy.

We present a comparative study of the glass forming ability of binary systems with varying composition, where the systems have similar global crystalline structure (CsCl+fcc). Biased Monte Carlo simulations using umbrella sampling technique show that the free energy cost to create a CsCl nucleus increases as the composition of the smaller particles is decreased. We find that systems with comparatively lower free energy cost to form CsCl nucleus exhibit more pronounced pre-crystalline demixing near the liquid/crystal interface. The structural frustration between the CsCl and fcc crystal demands this demixing. We show that closer to the equimolar mixture, the entropic penalty for demixing is lower and a glass forming system may crystallize when seeded with a nucleus. This entropic penalty as a function of composition shows a non-monotonic behaviour with a maximum at a composition similar to the well known Kob-Anderson (KA) model. Although the KA model shows the maximum entropic penalty and thus maximum frustration against CsCl formation, it also shows a strong tendency towards crystallization into fcc lattice of the larger "A" particles which can be explained from the study of the energetics. Thus for systems closer to the equimolar mixture although it is the requirement of demixing which provides their stability against crystallization, for KA model it is not demixing but slow dynamics and the presence of the "B" particles make it a good glass former. The locally favoured structure around "B" particles is quite similar to the CsCl structure and the incompatibility of CsCl and fcc hinders the fcc structure growth in the KA model. Although the glass forming binary systems studied here are quite similar, differing only in composition, we find that their glass forming ability cannot be attributed to a single phenomenon.

Modeling the Complete Catalytic Cycle of Aspartoacylase.

The complete catalytic cycle of aspartoacylase (ASPA), a zinc-dependent enzyme responsible for cleavage of N-acetyl-l-aspartate, is characterized by the methods of molecular modeling. The reaction energy profile connecting the enzyme-substrate (ES) and the enzyme-product (EP) complexes is constructed by the quantum mechanics/molecular mechanics (QM/MM) method assisted by the molecular dynamics (MD) simulations with the QM/MM potentials. Starting from the crystal structure of ASPA complexed with the intermediate analogue, the minimum-energy geometry configurations and the corresponding transition states are located. The stages of substrate binding to the enzyme active site and release of the products are modeled by MD calculations with the replica-exchange umbrella sampling technique. It is shown that the first reaction steps, nucleophilic attack of a zinc-bound nucleophilic water molecule at the carbonyl carbon and the amide bond cleavage, are consistent with the glutamate-assisted mechanism hypothesized for the zinc-dependent hydrolases. The stages of formation of the products, acetate and l-aspartate, and regeneration of the enzyme are characterized for the first time. The constructed free energy diagram from the reactants to the products suggests that the enzyme regeneration, but not the nucleophilic attack of the catalytic water molecule, corresponds to the rate-determining stage of the full catalytic cycle of ASPA.

Sampling free energy surfaces as slices by combining umbrella sampling and metadynamics.

Metadynamics (MTD) is a very powerful technique to sample high-dimensional free energy landscapes, and due to its self-guiding property, the method has been successful in studying complex reactions and conformational changes. MTD sampling is based on filling the free energy basins by biasing potentials and thus for cases with flat, broad, and unbound free energy wells, the computational time to sample them becomes very large. To alleviate this problem, we combine the standard Umbrella Sampling (US) technique with MTD to sample orthogonal collective variables (CVs) in a simultaneous way. Within this scheme, we construct the equilibrium distribution of CVs from biased distributions obtained from independent MTD simulations with umbrella potentials. Reweighting is carried out by a procedure that combines US reweighting and Tiwary-Parrinello MTD reweighting within the Weighted Histogram Analysis Method (WHAM). The approach is ideal for a controlled sampling of a CV in a MTD simulation, making it computationally efficient in sampling flat, broad, and unbound free energy surfaces. This technique also allows for a distributed sampling of a high-dimensional free energy surface, further increasing the computational efficiency in sampling. We demonstrate the application of this technique in sampling high-dimensional surface for various chemical reactions using ab initio and QM/MM hybrid molecular dynamics simulations. Further, to carry out MTD bias reweighting for computing forward reaction barriers in ab initio or QM/MM simulations, we propose a computationally affordable approach that does not require recrossing trajectories. © 2016 Wiley Periodicals, Inc.

Mechanism of Slow Crystal Growth of Tetrahydrofuran Clathrate Hydrate

Tetrahydrofuran (THF) clathrate hydrate has been frequently used in experimental studies instead of gas hydrates because it forms at a temperature higher than the ice point under ambient pressure. In this paper, we compare the crystal growth rates of THF hydrate and ice using molecular dynamics simulations. It is demonstrated that the crystal growth of THF hydrate is much slower than that of ice. The growth rates of THF hydrate significantly deviate from a standard kinetic model known as the Wilson–Frenkel model, whereas it reproduces the temperature dependence of the growth rate of ice. The slow crystal growth and the deviation from the Wilson–Frenkel model are attributed to the trapping of THF molecules in open small cages at the hydrate surface. We calculate the free energy profile of a THF molecule transferring from the bulk solution phase to the hydrate surface using the umbrella sampling technique. It is shown that a THF molecule trapped in an open small cage needs to cross one or two free energy ba...

Conformation and Aggregation of LKα14 Peptide in Bulk Water and at the Air/Water Interface.

Historically, the protein folding problem has mainly been associated with understanding the relationship between amino acid sequence and structure. However, it is known that both the conformation of individual molecules and their aggregation strongly depend on the environmental conditions. Here, we study the aggregation behavior of the model peptide LKα14 (with amino acid sequence LKKLLKLLKKLLKL) in bulk water and at the air/water interface. We start by a quantitative analysis of the conformational space of a single LKα14 in bulk water. Next, in order to analyze the aggregation tendency of LKα14, by using the umbrella sampling technique we calculate the potential of mean force for pulling a single peptide from an n-molecule aggregate. In agreement with the experimental results, our calculations yield the optimal aggregate size as four. This equilibrium state is achieved by two opposing forces: Coulomb repulsion between the lysine side chains and the reduction of solvent accessible hydrophobic surface area upon aggregation. At the vacuum/water interface, however, even dimers of LKα14 become marginally stable, and any larger aggregate falls apart instantaneously. Our results indicate that even though the interface is highly influential in stabilizing the α-helix conformation for a single molecule, it significantly reduces the attraction between two LKα14 peptides, along with their aggregation tendency.

Molecular view of the interaction of S-methyl methanethiosulfonate with DPPC bilayer

We present molecular dynamics (MD) simulation studies of the interaction of a chemo preventive and protective agent, S-methyl methanethiosulfonate (MMTS), with a model bilayer of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC). We analyzed and compared its diffusion mechanisms with the related molecule dimethyl sulfoxide (DMSO).We obtained spatially resolved free energy profiles of MMTS partition into a DPPC bilayer in the liquid-crystalline phase through potential of mean force (PMF) calculations using an umbrella sampling technique. These profiles showed a minimum for MMTS close to the carbonyl region of DPPC. The location of MMTS molecules in the DPPC bilayer observed in the MD was confirmed by previous SERS studies [1]. We decomposed PMF profiles into entropic and enthalpic contributions. These results showed that the driving force for the partitioning of MMTS into the upper region of DPPC is driven by a favorable entropy change while partitioning into the acyl chains is driven by enthalpy. On the other hand, the partition of DMSO into the membrane is not favored, and is driven by entropy instead of enthalpy. Free diffusion MD simulations using all atom and coarse grained (CG) models of DPPC in presence of MMTS were used to analyze the effect of DPPC-MMTS interaction. Density profiles showed that MMTS locates preferentially in the carbonyl region, as expected according to the PMF profile and the experimental evidence. MMTS presented two differential effects over the packing of DPPC hydrocarbonate chains at low or at high molar ratios. An ordering effect was observed when a CG MMTS model was used. Finally, free diffusion MD and PMF decomposition for DMSO were used for comparison.

Extreme bendability of DNA double helix due to bending asymmetry.

Experimental data of the DNA cyclization (J-factor) at short length scales exceed the theoretical expectation based on the wormlike chain (WLC) model by several orders of magnitude. Here, we propose that asymmetric bending rigidity of the double helix in the groove direction can be responsible for extreme bendability of DNA at short length scales and it also facilitates DNA loop formation at these lengths. To account for the bending asymmetry, we consider the asymmetric elastic rod (AER) model which has been introduced and parametrized in an earlier study [B. Eslami-Mossallam and M. R. Ejtehadi, Phys. Rev. E 80, 011919 (2009)]. Exploiting a coarse grained representation of the DNA molecule at base pair (bp) level and using the Monte Carlo simulation method in combination with the umbrella sampling technique, we calculate the loop formation probability of DNA in the AER model. We show that the DNA molecule has a larger J-factor compared to the WLC model which is in excellent agreement with recent experimental data.

Identification of Possible Binding Sites for Morphine and Nicardipine on the Multidrug Transporter P-Glycoprotein Using Umbrella Sampling Techniques.

The multidrug transporter P-glycoprotein (P-gp) is central to the development of multidrug resistance in cancer. While residues essential for transport and binding have been identified, the location, composition, and specificity of potential drug binding sites are uncertain. Here molecular dynamics simulations are used to calculate the free energy profile for the binding of morphine and nicardipine to P-gp. We show that morphine and nicardipine primarily interact with key residues implicated in binding and transport from mutational studies, binding at different but overlapping sites within the transmembrane pore. Their permeation pathways were distinct but involved overlapping sets of residues. The results indicate that the binding location and permeation pathways of morphine and nicardipine are not well separated and cannot be considered as unique. This has important implications for our understanding of substrate uptake and transport by P-gp. Our results are independent of the choice of starting structure and consistent with a range of experimental studies.

Excited state free energy calculations of Cy3 in different environments

Cy3, a cyanine dye, is one of the most widely used dyes in investigating the structure and dynamics of biomolecules by means of fluorescence methods. However, Cy3 fluorescence emission is strongly competed by trans-cis isomerization, whose efficiency is dictated by the isomerization energy barrier and the environment of Cy3. The fluorescence quantum yield of Cy3 is very low when the dye is free in homogeneous solution but it is considerably enhanced in an environment that rigidifies the structure, e.g. when it is attached to a DNA strand. In this work, the barriers for isomerization on the excited state of free Cy3, and Cy3 attached to single- and double-stranded DNA in methanol, are presented. The free energy and subsequently the isomerization barrier calculations are performed using the umbrella sampling technique with the weighted histogram analysis method. The hybrid quantum mechanics/molecular mechanics (QM/MM) approach is employed to provide the potential energy surfaces for the excited state dynamics simulations in umbrella sampling. The semiempirical floating occupation molecular orbital configuration interaction method is used for electronic excited state calculations of the QM region (Cy3). From the free energy calculations, the barrier of Cy3 attached to the single-stranded DNA is highest, in agreement with previously reported experimental results. This is likely due to the stacking interaction between Cy3 and DNA. Such a stacking interaction is likely associated with steric hindrance that prevents the rotation around the conjugated bonds of Cy3. If Cy3 experiences high steric hindrance, it has a higher isomerization barrier and thus the efficiency of fluorescence emission increases.

Why does Asn71 deamidate faster than Asn15 in the enzyme triosephosphate isomerase? Answers from microsecond molecular dynamics simulation and QM/MM free energy calculations.

Deamidation is the uncatalyzed process by which asparagine or glutamine can be transformed into aspartic acid or glutamic acid, respectively. In its active homodimeric form, mammalian triosephosphate isomerase (TPI) contains two deamidation sites per monomer. Experimental evidence shows that the primary deamidation site (Asn71-Gly72) deamidates faster than the secondary deamidation site (Asn15-Gly16). To evaluate the factors controlling the rates of these two deamidation sites in TPI, we have performed graphics processing unit-enabled microsecond long molecular dynamics simulations of rabbit TPI. The kinetics of asparagine dipeptide and two deamidation sites in mammalian TPI are also investigated using quantum mechanical/molecular mechanical tools with the umbrella sampling technique. Analysis of the simulations has been performed using independent global and local descriptors that can influence the deamidation rates: desolvation effects, backbone acidity, and side chain conformations. Our findings show that all the descriptors add up to favor the primary deamidation site over the secondary one in mammalian TPI: Asn71 deamidates faster because it is more solvent accessible, the adjacent glycine NH backbone acidity is enhanced, and the Asn side chain has a preferential near attack conformation. The crucial impact of the backbone amide acidity of the adjacent glycine on the deamidation rate is shown by kinetic analysis. Our findings also shed light on the effect of high-order structure on deamidation: the deamidation in a small peptide is favored first because of the higher reactivity of the asparagine residue and then because of the stronger stability of the tetrahedral intermediate.

Simple, yet powerful methodologies for conformational sampling of proteins.

Several biological functions, such as molecular recognition, enzyme catalysis, signal transduction, allosteric regulation, and protein folding, are strongly related to conformational transitions of proteins. These conformational transitions are generally induced as slow dynamics upon collective motions, including biologically relevant large-amplitude fluctuations of proteins. Although molecular dynamics (MD) simulation has become a powerful tool for extracting conformational transitions of proteins, it might still be difficult to reach time scales of the biological functions because the accessible time scales of MD simulations are far from biological time scales, even if straightforward conventional MD (CMD) simulations using massively parallel computers are employed. Thus, it is desirable to develop efficient methods to achieve canonical ensembles with low computational costs. From this perspective, we review several enhanced conformational sampling techniques of biomolecules developed by us. In our methods, multiple independent short-time MD simulations are employed instead of single straightforward long-time CMD simulations. Our basic strategy is as follows: (i) selection of initial seeds (initial structures) for the conformational sampling in restarting MD simulations. Here, the seeds should be selected as candidates with high potential to transit. (ii) Resampling from the selected seeds by initializing velocities in restarting short-time MD simulations. A cycle of these simple protocols might drastically promote the conformational transitions of biomolecules. (iii) Once reactive trajectories extracted from the cycles of short-time MD simulations are obtained, a free energy profile is evaluated by means of umbrella sampling (US) techniques with the weighted histogram analysis method (WHAM) as a post-processing technique. For the selection of the initial seeds, we proposed four different choices: (1) Parallel CaScade molecular dynamics (PaCS-MD), (2) Fluctuation Flooding Method (FFM), (3) Outlier FLOODing (OFLOOD) method, and (4) TaBoo SeArch (TBSA) method. We demonstrate applications of our methods to several biological systems, such as domain motions of proteins with large-amplitude fluctuations, conformational transitions upon ligand binding, and protein folding/refolding to native structures of proteins. Finally, we show the conformational sampling efficiencies of our methods compared with those by CMD simulations and other previously developed enhanced conformational sampling methods.

Exploring the local elastic properties of bilayer membranes using molecular dynamics simulations.

Membrane mechanical elastic properties regulate a variety of cellular processes involving local membrane deformation, such as ion channel function and vesicle fusion. In this work, we used molecular dynamics simulations to estimate the local elastic properties of a membrane. For this, we calculated the energy needed to extract a DOPE lipid molecule, modified with a linker chain, from a POPC bilayer membrane using the umbrella sampling technique. Although the extraction energy entails several contributions related not only to elastic deformation but also to solvation, careful analysis of the potential of mean force (PMF) allowed us to dissect the elastic contribution. With this information, we calculated an effective linear spring constant of 44 ± 4 kJ·nm(-2)·mol(-1) for the DOPC membrane, in agreement with experimental estimates. The membrane deformation profile was determined independently during the stretching process in molecular detail, allowing us to fit this profile to a previously proposed continuum elastic model. Through this approach, we calculated an effective membrane spring constant of 42 kJ·nm(-2)·mol(-1), which is in good agreement with the PMF calculation. Furthermore, the solvation energy we derived from the data is shown to match the solvation energy estimated from critical micelle formation constants. This methodology can be used to determine how changes in lipid composition or the presence of membrane modifiers can affect the elastic properties of a membrane at a local level.

Nature of the effective interaction between dendrimers.

We have performed fully atomistic classical molecular dynamics simulations to calculate the effective interaction between two polyamidoamine dendrimers. Using the umbrella sampling technique, we have obtained the potential of mean force (PMF) between the dendrimers and investigated the effects of protonation level and dendrimer size on the PMF. Our results show that the interaction between the dendrimers can be tuned from purely repulsive to partly attractive by changing the protonation level. The PMF profiles are well-fitted by the sum of an exponential and a Gaussian function with the weight of the exponential function dominating over that of the Gaussian function. This observation is in disagreement with the results obtained in previous analytic [C. Likos, M. Schmidt, H. Löwen, M. Ballauff, D. Pötschke, and P. Lindner, Macromolecules 34, 2914 (2001)] and coarse-grained simulation [I. Götze, H. Harreis, and C. Likos, J. Chem. Phys. 120, 7761 (2004)] studies which predicted the effective interaction to be Gaussian.

The transition mechanism of DNA overstretching: a microscopic view using molecular dynamics.

The overstretching transition in torsionally unconstrained DNA is studied by means of atomistic molecular dynamics simulations. The free-energy profile as a function of the length of the molecule is determined through the umbrella sampling technique providing both a thermodynamic and a structural characterization of the transition pathway. The zero-force free-energy profile is monotonic but, in accordance with recent experimental evidence, becomes two-state at high forces. A number of experimental results are satisfactorily predicted: (i) the entropic and enthalpic contributions to the free-energy difference between the basic (B) state and the extended (S) state; (ii) the longitudinal extension of the transition state and (iii) the enthalpic contribution to the transition barrier. A structural explanation of the experimental finding that overstretching is a cooperative reaction characterized by elementary units of approximately 22 base pairs is found in the average distance between adenine/thymine-rich regions along the molecule. The overstretched DNA adopts a highly dynamical and structurally disordered double-stranded conformation which is characterized by residual base pairing, formation of non-native intra-strand hydrogen bonds and effective hydrophobic screening of apolar regions.

Free energy of PAMAM dendrimer adsorption onto model biological membranes.

We investigated the thermodynamic, structural, and dynamics changes in dendrimer-membrane systems during dendrimer adsorption to biological membrane systems by combining atomistic molecular dynamics simulations with umbrella sampling techniques to understand the atomistic interactions between the dendrimer and biological membranes. An ethylenediamine core polyamidoamine dendrimer (generation 3) with amine terminal groups and both zwitterionic dipalmitoyl-phosphatidyl-choline (DPPC) and anionic palmitoyl-oleoyl-phosphatidyl glycerol (POPG) lipid bilayer membranes were used as the model dendrimer and biological membranes, respectively, in this study. The free energy of the dendrimer adsorption onto two model membranes with different charge states was quantitatively determined. For the zwitterionic DPPC membrane, the dendrimer has a minimum free energy of approximately 50 kcal/mol, which is 15 kcal/mol higher than that observed in previous studies. The dominant contribution to the adsorption potential energy is the van der Waals attraction between the dendrimer and the DPPC membrane. However, the anionic POPG membrane pulls the positively charged dendrimer with an attractive mean force of about 200 pN, finally positioning the dendrimer in the membrane headgroup region. As a result of these strong attractive dendrimer and membrane interactions, the dendrimer structurally undergoes the transition from spherical to a pancake conformation, which slows its lateral mobility, especially in the presence of the POPG membrane. The bilayer lipid membranes are also perturbed by the dendrimer adsorption.

REMD and umbrella sampling simulations to probe the energy barrier of the folding pathways of engrailed homeodomain.

Proteins fold by diverse pathways which depend on the energy barriers involved in reaching different intermediates. There has been a lot of development in the theoretical aspects of protein folding, from force-field to simulation techniques. One such simulation approach is replica exchange molecular dynamics simulation (REMD), which provides an efficient conformational sampling method to understand the events involved in protein folding. In this study, an attempt is made to explore the folding funnel of engrailed homeodomain protein (EnHD) using REMD simulations. EnHD is a 54 residue long helix bundle protein which has a folding time of about 15μs. The protein was represented using the Amber United atom model in order to reduce the system size which helped to speed up the simulation. Individual replicas were simulated for 1.4-2μs making cumulative time of more than 100μs of REMD simulations. Free energy analysis was carried out to understand the folding behavior of EnHD protein. Effects of temperature range and exchange frequency in REMD simulations have been explored. In addition to this, multiple umbrella sampling (US) simulations of a total of 320ns were also carried out, followed by weighted histogram analysis method (WHAM) to investigate the energy barriers involved during the folding of various intermediates. US studies were also carried on mutational variants of EnHD protein to see effect of the mutations on the folding pathway of the protein. The use of US technique may be helpful for predicting fast folding mutants or protein engineering. The combination of REMD with US may help in understanding the energetics between multiple pathways of fast folding proteins and their mutant counterparts.